ci: update tests workflow to use centralized reusable workflow and auto-suggest formatting changes on PRs

[thazhemadam]

Follow up to #183.

[github-actions]

Benchmark Results

	master	ba4a3a5...	master/ba4a3a51af4fa9...
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK2()	6.52 ± 0.21 ms	6.57 ± 0.23 ms	0.993
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK3()	2.35 ± 0.093 ms	2.36 ± 0.081 ms	0.995
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK4()	0.822 ± 0.033 ms	0.825 ± 0.033 ms	0.996
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK5()	0.875 ± 0.038 ms	0.874 ± 0.037 ms	1
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK6()	0.988 ± 0.036 ms	0.985 ± 0.034 ms	1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.34 ± 0.11 ms	1.33 ± 0.12 ms	1.01
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	2.59 ± 0.21 ms	2.6 ± 0.2 ms	0.994
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0362 ± 0.0057 s	0.0362 ± 0.005 s	1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.118 ± 0.0043 s	0.118 ± 0.0048 s	0.997
Simple Pendulum/IIP/Shooting(Tsit5())	0.189 ± 0.0049 ms	0.189 ± 0.0053 ms	0.999
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK2()	0.0419 ± 0.002 s	0.0416 ± 0.00086 s	1.01
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK3()	12.2 ± 0.19 ms	11.9 ± 0.19 ms	1.02
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK4()	3.47 ± 0.088 ms	3.43 ± 0.08 ms	1.01
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK5()	3.55 ± 0.091 ms	3.5 ± 0.093 ms	1.01
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK6()	3.7 ± 0.1 ms	3.64 ± 0.11 ms	1.02
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.42 ± 0.94 ms	3.44 ± 0.92 ms	0.995
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.09 ± 1.3 ms	6.13 ± 1.4 ms	0.993
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.13 ± 0.013 s	0.132 ± 0.013 s	0.989
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.399 ± 0.0068 s	0.4 ± 0.0068 s	0.998
Simple Pendulum/OOP/Shooting(Tsit5())	0.754 ± 0.03 ms	0.765 ± 0.039 ms	0.986
time_to_load	5.96 ± 0.032 s	5.94 ± 0.019 s	1

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[ChrisRackauckas]

@ErikQQY is it sometimes an array sometimes an AbstractVectorOfArray? We should probably always make it an AbstractVectorofArray

[ErikQQY]

@ErikQQY is it sometimes an array sometimes an AbstractVectorOfArray? We should probably always make it an AbstractVectorofArray

We always use Vector{Vector}} type in the nonlinear problems constructing and solving, should we change all of them to the AbstractVectorOfArray type instead? That could make the recursive flatten and unflatten of a Vector{Vector} much easier.

[ChrisRackauckas]

Yes, Make it an AbstractDiffEqArray, since there's time associated with it as well.

[ChrisRackauckas]

@ErikQQY can you help with the completion of this?

[ErikQQY]

Sure, I will help to get this complete

[ErikQQY]

The errors in this PR are mostly caused by the deprecation of indexing methods in RecursiveArrayTools.jl:

There are two ways of specifying boundary conditions when constructing a BVProblem, e.g. bc(u,p,t)=[u[1][1]] or bc(u,p,t)=[u(10.0)[1]] before RecursiveArrayTools.jl deprecate u[1] for u.u[1] or u[:,1] kind indexing, both of them were working fine, but now the centralized CI errors are mostly caused by the deprecation of this API.

So here is the solution:

We need to change the convention of defining boundary conditions as bc(u,p,t)=[u.u[1][1]] or bc(u,p,t)=[u[:,1][1]] now for this PR to continue. This may involve lots of tests, examples, and docs change.

[ChrisRackauckas]

We need to change the convention of defining boundary conditions as bc(u,p,t)=[u.u[1][1]] or bc(u,p,t)=[u[:,1][1]] now for this PR to continue. This may involve lots of tests, examples, and docs change.

Yes, that's what needs to happen everywhere.

[ChrisRackauckas]

@avik-pal do you know why this ambiguity is still reported? I don't see it actually being hit?

[avik-pal]

https://github.com/SciML/BoundaryValueDiffEq.jl/blob/master/test/misc/qa_tests.jl#L5 needs to be removed

[ErikQQY]

The Windows CI test looks weird, all other tests are working fine